The short answer is: nowhere.
It is a relic of the past, where Microsoft intended developers to inherit all their custom exceptions from ApplicationException. Shortly after, they changed their mind and advised that custom exceptions should derive from the base Exception class. See Best Practices for Handling Exceptions on MSDN.
One of the more widely circulated reasons for this comes from an exerpt from Jeffery Richter in Framework Design Guidelines:
System.ApplicationException is a class that should not be part of the .NET Framework. The original idea was that classes derived from SystemException would indicate exceptions thrown from the CLR (or system) itself, whereas non-CLR exceptions would be derived from ApplicationException. However, a lot of exception classes didn't follow this pattern. For example, TargetInvocationException (which is thrown by the CLR) is derived from ApplicationException. So, the ApplicationException class lost all meaning. The reason to derive from this base class is to allow some code higher up the call stack to catch the base class. It was no longer possible to catch all application exceptions.
So there you have it. The executive summary is that ApplicationException is not harmful, just useless.